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Simplifying 40x2 + -30x + 135 = 0 Reorder the terms: 135 + -30x + 40x2 = 0 Solving 135 + -30x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(27 + -6x + 8x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(27 + -6x + 8x2)' equal to zero and attempt to solve: Simplifying 27 + -6x + 8x2 = 0 Solving 27 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.375 + -0.75x + x2 = 0 Move the constant term to the right: Add '-3.375' to each side of the equation. 3.375 + -0.75x + -3.375 + x2 = 0 + -3.375 Reorder the terms: 3.375 + -3.375 + -0.75x + x2 = 0 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + -0.75x + x2 = 0 + -3.375 -0.75x + x2 = 0 + -3.375 Combine like terms: 0 + -3.375 = -3.375 -0.75x + x2 = -3.375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -3.375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -3.375 + 0.140625 Combine like terms: -3.375 + 0.140625 = -3.234375 0.140625 + -0.75x + x2 = -3.234375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -3.234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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